Our motivation comes from recent interest in higher principal
bundles or gerbes [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
Recall that for a paracompact space \(M\) , there is a bijection
between \(H^3(M,\mathbb {Z})\)  and the set of equivalence classes of \(S^1\)  bundle gerbes
on \(M\) . An \(S^1\)  bundle gerbe on \(M\)  is, roughly speaking, a principal bundle on \(M\) 
where the structure group \(S^1\)  is replaced by the groupoid \(S^1\) , viewed
as a group object in the category of groupoids, or equivalently (via the nerve
construction) as a simplicial group \(NS^1\) . In Section  we explain how
\(S^1\)  bundle gerbes on \(M\)  are naturally viewed as simplicial principal bundles
(more precisely as principal twisted cartesian products)
for the simplicial topological group \(NS^1\) . From another point of view,
\(H^3(M,\mathbb {Z})\)  parametrizes the set of isomorphism classes of principal \(BS^1\)  bundles on
\(M\) . The process of passing from a simplicial principal bundle for \(NS^1\)  to
a principal \(BS^1\)  bundle is exactly the process of geometric realization.
